From rate distortion theory to metric mean dimension: variational principle

摘要

The purpose of this paper is to point out a new connection betweeninformation theory and dynamical systems. In the information theory side, weconsider rate distortion theory, which studies lossy data compression ofstochastic processes under distortion constraints. In the dynamical systemsside, we consider mean dimension theory, which studies how many parameters persecond we need to describe a dynamical system. The main results are newvariational principles connecting rate distortion function to metric meandimension.